Ch 7 Random Variables

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Chapter 7: Random Variables (Total Time: 14 Days)

• Discrete and Continuous Random Variables
KA 12:Introduction to Random Variables



o Introduction; discrete random variables
o Continuous random variables – uniform & normal
• Means and Variances of Random Variables

KA 5: Variance of a population



KA:6 Sample variance - Thinking about how we can estimate the variance of a population by looking at the data in a sample.


KA 86: Statistics: Variance of a Population


KA 87: Statistics: Sample Variance


KA 7: Review and intuition why we divide by n-1 for the unbiased sample variance



KA 8: Simulation showing bias in sample variance



Actual simulaion: Simulation showing bias in sample variance


KA 9: Simulation providing evidence that (n-1) gives us unbiased estimate
Actual simulaion: Will it converge to -1?



KA 74: Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance



KA 11:Statistics: Alternate Variance Formulas




o Mean and variance of a discrete random variable
o Law of large numbers; rules for means

KA 24:Law of Large Numbers

The mean of your sample is going to converge to the true mean of the population or to the expected value of the random variable.

Gambler's Fallacy



o Rules for variances and independence